Related papers: Free medial quandles

This is my dissertation about digraphs ordered by pp-constructability. We study in particular smooth digraphs, i.e., digraphs without sources or sinks, tournaments and semicomplete digraphs, orientations of paths and cycles, digraphs with…

We study flat vector bundles over complex parallelizable manifolds.

Let $D$ be a division ring infinite-dimensional over its center $k$ with multiplicative group $D^{\times}$. We show that if $D$ belongs to certain families, there exist free symmetric and unitary pairs in $D^{\times}$ with respect to a…

We give four constructions of non-$\partial\bar\partial$ (hence non-K\"ahler) manifolds: (1) A simply connected page-$1$-$\partial\bar\partial$-manifold (2) A simply connected $dd^c+3$-manifold (3) For any $r\geq 2$, a simply connected…

Motivated by questions in inverse scattering theory, we develop free boundary methods in obstacle problems where both the solution and the right hand side of the equation may have varying sign. The key condition that prevents the appearance…

A homology and cohomology theory for topological quandles are introduced. The relation between these (co)homology groups and quandle (co)homology groups are studied. The 1 - topological quandle cocycles are used to compute state sum…

We describe a glueing construction for a certain self-dual reduction of the Yang-Mills equations in dimension 8.

Given a Riemannian manifold and a closed submanifold, we find a geodesic segment with free boundary on the given submanifold. This is a corollary of the min-max theory which we develop in this article for the free boundary variational…

This paper is a survey on the structure of manifolds with a lower Ricci curvature bound.

In this paper, we introduce techniques for producing normal square-free monomial ideals from old such ideals. These techniques are then used to investigate the normality of cover ideals under some graph operations. Square-free monomial…

We give elementary constructions for Satake-Furstenberg, Martin and Karpelevich boundaries of symmetric spaces. We also consruct some "new" boundaries

We establish a canonical correspondence between connected quandles and certain configurations in transitive groups, called quandle envelopes. This correspondence allows us to efficiently enumerate connected quandles of small orders, and…

In this article, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of such racks and quandles are precisely those automorphisms that…

We construct anomaly free non-supersymmetric large N gauge theories from orientifolds of Type IIB on C^3/G orbifolds. In particular, massless as well as tachyonic one-loop tadpoles are cancelled in these models. This is achieved by starting…

We survey techniques for constructing spaces with non-trivial self covers. These processes include methods for building low and high dimension continua which non-trivially self. We also discuss several related group theoretic and…

First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth…

This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.

In this paper we survey $n$-dimensional solenoidal manifolds for $n=1,2$ and 3, and present new results about them. Solenoidal manifolds of dimension $n$ are metric spaces locally modeled on the product of a Cantor set and an open…

We construct compact polyhedra with $m$-gonal faces whose links are generalized 3-gons. It gives examples of cocompact hyperbolic bildings of type $P(m,3)$. For $m=3$ we get compact spaces covered by Euclidean buildings of type $A_2$.

For all $m > 0$ we build a two-dimensional family of smooth manifolds of real dimension $3m + 2$ and use it to interpolate between the anticanonical family in the complex projective space of dimension $m + 1$ and its mirror dual. The main…